A principle of virtual work for combined electrostatic and mechanical loading of materials

McMeeking, Robert M.; Landis, Chad M.; Jiménez, Salomón M.A.

doi:10.1016/j.ijnonlinmec.2007.03.008

Cited by 85 publications

(64 citation statements)

References 14 publications

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“…Moreover, it satisfies the Volterra property by virtue of (28). Still by (28), the operator P can be extended to C[0, T ], and if Hypothesis 3.3 (i) is fulfilled, then the Lipschitz property (22) holds.…”

Section: Inversion Of Hysteresis Operators With Time Dependent Coeffimentioning

confidence: 99%

“…Still by (28), the operator P can be extended to C[0, T ], and if Hypothesis 3.3 (i) is fulfilled, then the Lipschitz property (22) holds. The main result of this section reads as follows.…”

Section: Inversion Of Hysteresis Operators With Time Dependent Coeffimentioning

confidence: 99%

“…(2) Micromechanical models that consider the material on the level of single grains, see, for example, Delibas et al [9], Fröhlich [10], Huber and Fleck [13], Belov and Kreher [4], Huber [12], McMeeking et al [28], Smith and Hu [35].…”

Section: Introductionmentioning

confidence: 99%

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A thermodynamically consistent phenomenological model for ferroelectric and ferroelastic hysteresis

Kaltenbacher

Krejčı́

2015

Z. Angew. Math. Mech.

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We propose a hysteretic model for electromechanical coupling in piezoelectric materials, with the strain and the electric field as inputs and the stress and the polarization as outputs. This constitutive law satisfies the thermodynamic principles and exhibits good agreement with experimental measurements. Moreover, when it is coupled with the mechanical and electromagnetic balance equations, the resulting PDE system is well-posed under the hypothesis that hysteretic effects take place only in one preferred direction. We prove the existence and uniqueness of its global weak solutions for each initial data with prescribed regularity. One of the tools is a new Lipschitz continuity theorem for the inverse Preisach operator with time dependent coefficients.

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Section: Inversion Of Hysteresis Operators With Time Dependent Coeffimentioning

confidence: 99%

Section: Inversion Of Hysteresis Operators With Time Dependent Coeffimentioning

confidence: 99%

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A thermodynamically consistent phenomenological model for ferroelectric and ferroelastic hysteresis

Kaltenbacher

Krejčı́

2015

Z. Angew. Math. Mech.

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“…In finding the deformed state of the body under consideration (the spatial motion problem), the resulting electric field must be computed. In computing the resulting electric field, the free space surrounding the body should in principle be taken into account by using for example the formulas proposed in [15][16][17]. However, it is a well-known fact that for many materials the surrounding free space can be conveniently ignored because of its negligible contribution.…”

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confidence: 99%

On the spatial and material motion problems in nonlinear electro-elastostatics with consideration of free space

Steinmann

2012

Mathematics and Mechanics of Solids

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In this work the formulation of spatial and material motion problems in nonlinear electro-elastostatics is considered using an energy approach, which takes into account the contribution of the free space surrounding a nonlinearly polarized body undergoing large deformation. The free space can have a huge impact on the electric field and on the deformation field inside a body made of materials with low electric permittivity such as the so-called electronic electroactive polymers (EEAPs). The contribution of the free space can be taken into account by using the electric flux and the Maxwell's traction acting on the boundary of the body. These two quantities can be expressed in terms of a stored energy density function. By using a stored energy density function for both the material body and the (finite or infinite) free space, the governing equations of both spatial and material motion problems are derived by considering the change of energy with respect to a change in the spatial or material configuration. In the spatial motion problem, well-known definitions for electric and mechanical quantities are derived. In the material motion problem, in addition to the derivation of configurational forces, this approach reveals the formulas for the part of energy that is released from the system material body, applied forces in response to a change in the material configuration, which are particularly useful in the study of defects such as crack propagation. The same approach can be used in the case of nonlinear electro-thermo-mechanical coupling and constitutes the direction for future works.

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“…(2) Micromechanical models that consider the material on the level of single grains, see, e.g., Belov & Kreher (2006); Delibas et al (2005); Fröhlich (2001); Huber (2006); Huber & Fleck (2001); McMeeking et al (2007).…”

Section: Introductionmentioning

confidence: 99%

Modeling and Numerical Simulation of Ferroelectric Material Behavior Using Hysteresis Operators

Kaltenbacher¹

2011

Ferroelectrics - Characterization and Modeling

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A principle of virtual work for combined electrostatic and mechanical loading of materials

Cited by 85 publications

References 14 publications

A thermodynamically consistent phenomenological model for ferroelectric and ferroelastic hysteresis

A thermodynamically consistent phenomenological model for ferroelectric and ferroelastic hysteresis

On the spatial and material motion problems in nonlinear electro-elastostatics with consideration of free space

Modeling and Numerical Simulation of Ferroelectric Material Behavior Using Hysteresis Operators

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